Place Value and Number Sense

Every digit in a number has a value that depends on its position. The 3 in 300 is worth ten times more than the 3 in 30, which is worth ten times more than the 3 in 3. This is the place value system — the foundation that makes all of arithmetic work.

The Place Value Chart

Each position is 10 times the value of the position to its right:

Example 1: Identify Place Values in 47,253

• The 4 is in the ten thousands place — its value is $40{,}000$
• The 7 is in the thousands place — its value is $7{,}000$
• The 2 is in the hundreds place — its value is $200$
• The 5 is in the tens place — its value is $50$
• The 3 is in the ones place — its value is $3$

Expanded form: $47{,}253 = 40{,}000 + 7{,}000 + 200 + 50 + 3$

Reading and Writing Large Numbers

Use commas to group digits into sets of three, starting from the right. Each group has a name:

Example 2: Read 3,502,170

Group it: 3 million, 502 thousand, 170

Read it as: “three million, five hundred two thousand, one hundred seventy”

Example 3: Write “twelve million, forty thousand, nine hundred six” as a number

• Twelve million = 12,000,000
• Forty thousand = 40,000
• Nine hundred six = 906

$12{,}040{,}906$

Comparing Whole Numbers

To compare two numbers, start from the leftmost digit and compare place by place:

Example 4: Compare 4,387 and 4,312

• Thousands place: both have 4 — tied
• Hundreds place: both have 3 — tied
• Tens place: 8 vs 1 — 8 is larger

$4{,}387 > 4{,}312$

Example 5: Compare 52,100 and 6,999

$52{,}100$ has 5 digits, $6{,}999$ has 4 digits. The number with more digits is always larger (for whole numbers).

$52{,}100 > 6{,}999$

Ordering Numbers

To arrange numbers from least to greatest (or greatest to least), compare them systematically:

Example 6: Order 1,450; 14,500; 1,054; 1,540 from least to greatest

First, separate by digit count:

• 4-digit numbers: 1,054; 1,450; 1,540
• 5-digit number: 14,500

Among the 4-digit numbers, compare from the left:

• All start with 1, so compare hundreds: 0 < 4 < 5

Answer: $1{,}054 < 1{,}450 < 1{,}540 < 14{,}500$

The Number Line

The number line is a visual tool that puts numbers in order. Numbers increase as you move right and decrease as you move left.

Key ideas:

• Every whole number has a unique position on the number line
• The distance between any two consecutive whole numbers is the same
• You can use the number line to estimate, compare, and visualize operations

Zero as a Placeholder

Zero holds a place open. Without it, 305 would collapse into 35 — a completely different number.

$305 \neq 35$

The zero in 305 means “no tens” while keeping the 3 in the hundreds place and the 5 in the ones place.

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Each digit’s value depends on its position in the number
• Each place is 10 times the value of the place to its right
• Commas group digits into thousands, millions, billions for readability
• Compare numbers by starting from the leftmost digit
• Zero is a placeholder — it holds positions that have no value but keeps other digits in the correct place

Return to Arithmetic for more foundational math topics.